Multi-focal diffractive ophthalmic lenses

ABSTRACT

A multifocal ophthalmic lens has diffractive power produced by a plurality of concentric zones. The zones have radii that meet the condition 
     
         R.sub.0.sup.2 is not equal to R.sub.1.sup.2 -R.sub.0.sup.2 
    
     where R 0  is the radius of the central zone and R 1  is the radius of the first annular zone.

This is a continuation of application Ser. No. 176,701, filed Apr. 1,1988, now abandoned.

FIELD OF THE INVENTION

The present invention relates to ophthalmic lenses having a plurality offocal lengths.

BACKGROUND OF THE INVENTION

As used herein the term "ophthalmic lens" means vision correction lensessuch as contact lenses and intraocular lenses. Other, less common,vision correction lenses such as artificial corneas and intralamellarimplants are also included in this definition.

Bifocal spectacle lenses have been known for hundreds of years. In suchlenses a first region of the lens is typically provided with a firstfocal length while a second region of the lens is provided with a secondfocal length. The user looks through the appropriate portion of the lensfor viewing near or far objects.

More recently there has been interest in developing other types ofmultifocal ophthalmic lenses. Multi-focal contact lenses utilizing anapproach similar to that used in spectacle lenses are described inContact Lenses: A Textbook for Practitioner and Student, Second Edition,Volume 2 on pages 571 through 591. Such lenses have serious drawbacks,however, because they require that the lens shift on the eye so thatdifferent portions of the lens cover the pupil for distant and closevision. This design cannot be used for intraocular lenses or otherimplanted lenses, because such lenses cannot shift. Even for contactlenses the design is disadvantageous because it is difficult to insurethat the lens will shift properly on the eye for the desired range ofvision.

In another design for a bifocal contact lens described in theabove-referenced textbook, a central zone of the lens is provided with afirst focal length and the region surrounding the central zone isprovided with a second focal length. This design eliminates thenecessity for shifting the lens by utilizing the phenomenon ofsimultaneous vision. Simultaneous vision makes use of the fact that thelight passing through the central zone will form an image at a firstdistance from the lens and light passing through the outer zone willform an image at a second distance from the lens. Only one of theseimage locations will fall on the retina and produce a properly focusedimage while the other image location will be either in front of orbehind the retina. The human eye and brain will, to a great extent, worktogether to ignore the improperly focused image. Thus the user of such alens receives the subjective impression of a single well-focused image.A disadvantage of such a lens is that, if the central zone is made largeenough to provide sufficient illumination in its associated image in lowlight situations, i.e. when the patient's pupil is dilated, the centralzone will occupy all or most of the pupil area when the pupil contractsin a bright light situation. Thus bifocal operation is lost in brightlight. Conversely if the central zone is made small enough to providebifocal operation in bright light situations, an inadequate amount ofthe light will be directed to the image associated with the central zonein low light environments. Because the central zone is commonly used toprovide distant vision, this can create a dangerous situation when theuser of such a lens requires distant vision in low light situations suchas when the user must drive a motor vehicle at night.

U.S. Pat. Nos. 4,210,391; 4,340,283; and 4,338,005, all issued to Cohen,teach the use of a plurality of annular regions that direct light tomultiple foci and rely upon simultaneous vision to discard unfocusedimages. They teach the use of alternating concentric Fresnel zones,wherein each of those zones have substantially equal area. The use ofsuch equal area zones causes the lens to provide a diffractive focus ofthe light. A first focus will occur for the zero order diffracted lightwhile a second focus will occur for the first order diffracted light.Such a structure is known as a diffractive zone plate.

A diffractive zone plate must be designed for light of a particularwavelength and will work most efficiently for light at that wavelength.The radius of the n^(th) zone (r_(n)) in the diffractive zone platestaught in the Cohen patents will be equal to √n r₁ where r₁ is theradius of the central zone. To a reasonable approximation r₁ would beequal to √λf where λ is the design wavelength and f is the focal lengthof the diffractive structure. Therefore the n^(th) zone would have aradius equal to √nλf.

In designing a diffractive zone plate a design wavelength must beselected. When a desired focal length and wavelength are selected for alens as taught in the Cohen patents, the area of each of the zones, andthus the location of the boundary of each zone, are determined. Thisrigid definition of the zones result in a disadvantage to the zone platestructure. In order to obtain an efficient diffractive bifocaloperation, a sufficient number of zones must be used. However if thearea of the central zone is too large, under bright light situationswith the pupil constricted, only a single zone or very few zones will beutilized. Thus the efficiency of the multi-focal operation is greatlyreduced.

SUMMARY OF THE INVENTION

The present invention provides a multifocal ophthalmic lens havingoptical power, at least a portion of the optical power being produced bydiffraction. The lens has a plurality of diffractive zones including acircular central zone and a plurality of concentric annular zones. Thecentral zone has a radius r₀ and the first annular zone has a radius r₁where r₁ ² -r₀ ² is not equal to r₀ ².

The present invention recognizes that the central zone of an ophthalmiclens utilizing a phase zone plate need not have the same area as theother zones. In one embodiment the central zone is made smaller than theother zones in order to insure adequate multifocal operation. In anotherembodiment the size and refractive power of the central zone is adjustedto control the distribution of energy between the foci.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front view of a lens having a flat surface constructed inaccordance with the present invention;

FIG. 2 is a schematic diagram for use in describing the invention;

FIG. 3 is a cross-sectional view of a single zone of the lens of FIG. 1;

FIG. 4 is a cross-sectional view of a meniscus lens constructed inaccordance with the present invention;

FIG. 5 is a cross-sectional view of a single zone of the lens of FIG. 4;

FIG. 6 is a schematic diagram of a lens for use in describing thederivation of the equation for curved surface corrections to zone radii;and

FIG. 7 is a cross-sectional view of a biconvex lens constructed inaccordance with the present invention.

DETAILED DESCRIPTION

An ophthalmic lens, generally designated 10 in FIG. 1, is provided witha diffractive zone plate including zones 12, 14, 16, 18, and 20.Although the drawing shows only five zones, more would typically beprovided. The exact number would depend on the amount of change from thebase optical power of the lens, the size of the lens and the designwavelength, among other factors. Typical lenses have between 20 and 30zones. As will be described below the radii of the zones will beaffected by several factors including the choice of a design wavelength.In a preferred embodiment the design wavelength is chosen in thespectral region of the greatest photopic sensitivity of the human eye.

The lens of FIG. 1 typically has a base optical power provided byrefraction. An additional power is provided by diffraction.Alternatively the entire optical power could be provided by diffraction.The diffractive optical power is provided by separating the zones byoptical steps. An optical step causes light rays passing immediately oneach side thereof to experience different optical path lengths, wherethe optical path length is defined in terms of wavelengths of light of adesign wavelength. One way of providing optical steps is to providephysical structures on a surface of the lens. Alternatively opticalsteps may be provided on a smooth surface by varying the index ofrefraction of the underlying material. Such variation of the index ofrefraction may be accomplished, for example, by removing portions of thelens material and filling the structures formed thereby with a materialhaving a different index of refraction or by doping portions of the lenswith a dopant that causes the index of refraction of the doped regionsto change.

The size of the optical steps is defined in terms of optical height. Theoptical height of a step should be an odd half integral multiple of thewavelength of light of the design wavelength. Typically the opticalheight is one half wavelength for light of the design wavelength. Theterm optical height, as used herein, refers to the difference in opticalpath length in terms of wavelengths of light, for adjacent light rayspassing on each side of the step. Thus to provide an optical height ofone-half wavelength, the actual height should be (λ/2)/(i_(i) -i₂) whereλ is the wavelength of the light in question, n₁ is the first index ofrefraction, typically that of the lens material, and i₂ is the secondindex of refraction, that of the medium bordering the lens or of themodified portion of the lens.

In order for the lens to exhibit diffractive power, a required conditionis that rays of light passing through the edges of the zones arrive atthe image point in phase. Thus the optical path length difference for aray of light passing through the outer edge of a zone should be onewavelength less than that for a ray of light passing through the outeredge of the next zone. As previously described this requirement has inthe prior art led to the conclusion that the radii of all zones areuniquely determined when a design wavelength, a focal length, and theindices of refraction are chosen. This conclusion is unduly restrictive.

FIG. 2 will be used to show that more freedom is available in selectingzone radii than taught by the prior art. The example shown in FIG. 2represents the special case of diffractive zones provided on anotherwise flat surface. In some ophthalmic lenses, such as intraocularlenses, the zones may actually be provided on a flat surface. In othersthe radius of curvature of the surface is great enough that it may beneglected.

In FIG. 2, z represents the distance from an object to the lens alongthe optical axis of the lens and z' represents the distance from thelens to the image location along that axis. The distance represented bys₀ is the distance from the object to the outer edge of the central zoneand that represented by t₀ is the distance from the outer edge of thecentral zone to the image location. Similarly s_(n) represents thedistance from the object to the outer edge of the n^(th) zone and t_(n)represents the distance from the outer edge of the n^(th) zone to theimage. The effect of the unnecessary restriction of the prior art is torequire that s₀ equal z and t₀ equal z'. Instead, as previouslyexplained, the proper requirement is that the optical path lengthdifference from the outer edge of one zone to the outer edge of the nextzone must be one wavelength. In order for this condition to be met, thefollowing relationship must hold:

    s.sub.0 μ.sub.1 +t.sub.o μ.sub.2 +nλ=s.sub.n μ.sub.1 +t.sub.n μ.sub.2                                       (1)

where μ₁ is the index of refraction of the medium through which the rayss₀ and s_(n) travel, μ₂ is the index of refraction of the medium throughwhich the rays t₀ and t_(n) travel and λ is the design wavelength.

Using the Pythagorean theorem equation (1) may be rewritten as: ##EQU1##where r₀ is the radius of the central zone and r_(n) is the radius ofthe n^(th) zone. Thus the radius of the central zone may be arbitrarilychosen and equation (2) solved to determine the radii of the remainingzones to provide the desired diffractive power. As an approximation,equation (2) may be expressed as:

    r.sub.n.sup.2 =r.sub.0.sup.2 +2nλf                  (3)

where f is the focal length of the portion of the optical power of thelens provided by the diffractive structure.

The ability to arbitrarily select the radius of the central zone whileproviding diffractive optical power can be expressed in terms of therelationships among the radii of the zones. If the radius of the centralzone is designated r₀, the radius of the innermost annular zone isdesignated r₁ and the radius of the second annular zone is designatedr₂, the conditions previously described may be expressed by saying thatr₀ ² is not equal to r₁ ² -r₀ ² and r₂ ² -r₁ ² is equal to r₁ ² -r₀ ².In general, r_(n) ² -r_(n-1) ² is equal to r_(n-1) ² -r_(n-2) ² forvalues of n greater than or equal to 2.

Since the radius of central zone 12 of FIG. 1 may be chosen arbitrarily,it may be made smaller than the prior art dictates, causing theremaining zones to be moved closer to the center of the lens. Then evenwhen the pupil of the eye is constricted, as in a bright-lightsituation, a sufficient number of zones will be used to allow multifocaloperation of the lens.

If the design wavelength, the focal length and the pupil size of thepatient are such that an adequate number of zones can be provided whilemaking the central zone larger than the other zones, such a design isacceptable. If such a design is possible for a particular patient, otheradvantages may be achieved. For example a zone plate having a differentfocal length, design wavelength or both could be provided within thecentral zone. Such an additional zone plate could be used as a method ofredistributing the light energy between the foci.

Another advantage of the invention lies in the ability to redistributethe proportion of the light directed to each focus without the use ofanother diffractive structure in the central zone. By providing adifferent refractive power in the central zone than that provided in theremainder of the lens, light passing through the central zone can bedirected to either of the foci produced by the combined refractive anddiffractive power of the remainder of the lens. By adjusting the size ofthe central zone and the focus to which it directs light, the energydistribution between the foci may be optimized. Thus a patient who mustdrive a vehicle in low light conditions might require more energy in thefar object focus while another patient who does delicate work mightrequire that more energy be provided to the near focus.

FIG. 3 shows a cross-sectional view of a single zone of a lens as itwould be shaped on the flat surface of the lens of FIG. 1. Those skilledin the art will readily perceive that the vertical scales in FIGS. 3through 5 and 7 are greatly exaggerated in order to more clearly showthe nature of the structures. The anterior side 30 is smooth while thediffractive zones are provided on the posterior side 32. Posterior side32 includes diffractive zone 34 and step 36. As previously described theoptical height of step 36 is λ/2, where λis the design wavelength. Thediffractive zone formed by region 34 and step 36 leaves a cut outsection 38 in the posterior side 32 of the lens. As previouslydescribed, region 38 may be left open or may be filled with a materialhaving a different index of refraction from that of the lens body.

The shape of the zone surface will affect the diffractive orders towhich energy is directed by the structure and the energy distributionamong those orders. In a preferred embodiment the shape of region 34 ofthe illustrated zone is parabolic. The precise shape of the zone is,however, less important to the performance of the lens than thelocations of the zone boundaries. The key requirements are that the zoneboundaries be properly located and that the zone curves smoothly. Sincea spherical zone shape is generally easier to generate than a parabolicone using currently available techniques and a sphere is a reasonablyclose approximation to a parabola over a small region, a spherical zoneshape may be used to approximate the parabola. The spheres that are usedin the preferred embodiment are designed in such a manner that theproper step height will be provided between the zones and the center ofthe spheres lie on the optical axis of the lens. Other shapes may alsobe used as long as such shapes are a good approximation to a parabola.

FIG. 4 shows a cross-sectional view through the center of a curved lens40 constructed in accordance with one embodiment of the invention. Thelens is a meniscus lens having a smooth anterior side 42 and adiffractive zone plate formed by a structured posterior side 44 having aseries of diffractive zones 46, 48, 50, 52 and 54. Alternatively thezones could be formed on the anterior side 40 of the lens, or even onboth sides of the lens. As previously described the optical stepsseparating the diffractive zones such as optical step 56 could also beformed in other ways not requiring an actual physical step.

FIG. 5 illustrates the zone shape for the curved lens 40 of FIG. 4. Thezone shown in FIG. 5 has a region 60 and a step 62. The optical heightof step 62 is again λ/2 for the design wavelength. Also shown in FIG. 5is dashed line 64 that represents the base curve of the lens (i.e. thecurve that the lens surface would follow if no diffractive zones wereprovided). The shape of region 60 is determined in a manner similar tothat of region 34 of FIG. 3.

When the zones are provided on a curved surface, improved performancemay be obtained by introducing a correction for the curvature. Thederivation of the curved surface correction will be more readilyunderstood by reference to FIG. 6. A term δ is introduced representingthe difference in optical path length experienced by a light raytraveling from the object to the edge of the central zone to the imagelocation and a light ray traveling along the optical axis. The value ofδ is given by:

    δ=s.sub.0 μ.sub.1 +t.sub.0 μ.sub.2 -(zμ.sub.1 +z'μ.sub.2)(4)

where s₀ is the distance from the object to the edge of the centralzone, t₀ is the distance from the edge of the central zone to the imagelocation, z is the distance from the object to the lens along theoptical axis, z' is the distance from the lens to the image locationalong the optical axis and μ₁ and μ₂ are the indices of refractionthrough which the s₀ and t₀ beams travel, respectively.

The values of z and z' are chosen for the case of an image of an objectclose to the eye being focused on the retina by the near object focalpower of the lens. Typically the physical object is located 30 to 40 cmfrom the eye. The object distance for these equations, however, is thedistance to the image produced by the refractive power of the lens incombination with the cornea. When the object location is on the sameside of the lens as the image location, z takes on a negative value. Fora contact lens the value of z would typically be about -32 mm and thevalue of z' would be about 30 mm. For an intraocular lens the value of zwould typically be about -20 mm and the value of z' would be about 19mm.

As previously described the optical path length difference from theouter edge of a zone to the outer edge of the next zone should be λ,where λ is the design wavelength. From this the optical equation for then^(th) zone may be written as follows:

    zμ.sub.1 +z'μ.sub.2 +nλ+δ=s.sub.n μ.sub.1 +t.sub.n μ.sub.2                                                (5)

where s_(n) and t_(n) are the distances from the object to outer edge ofthe n^(th) zone and from the outer edge of the n^(th) zone to the imagelocation, respectively. This equation can be rewritten as:

    zμ.sub.1 +z'μ.sub.2 +μλ=s.sub.n μ.sub.1 +t.sub.n μ.sub.2                                                (6)

where

    ν=n+δ/λ,                                   (7)

From geometric considerations, it may be shown ##EQU2## where h_(n) isthe distance from a plane tangent to the lens on the optic axis to thelens at the outer edge of the n^(th) zone and may be calculated by##EQU3## where R_(c) is the radius of curvature of the lens.

Substituting the values from equations 8, 9, and 10 into equation 6 andsquaring twice yields:

    r.sub.n.sup.4 (c.sub.2.sup.2 -c.sub.3.sup.2)-r.sup.2 [2c.sub.1 c.sub.2 +c.sub.3.sup.2 (d.sup.2 +d'.sup.2)]+c.sub.1.sup.2 -d.sup.2 d'.sup.2 =0(11)

where

d=(z+h_(n)),

d'=(z'-h_(n)),

c₁ =(zμ₁ +z'μ₂ +νλ)² -d² μ₁ ² +d'² μ₂ ²,

c₂ =μ₁ ² +μ₂ ², and

c₃ =2μ₁ μ₂

This equation may be solved by iterative techniques. As previouslydescribed the object and image are effectively on the same side of thelens for a typical diffractive structure used in an ophthalmic lens.Therefore μ₁ and μ₂ are equal and the symbol μ may be substituted forboth. Using this substitution and other approximations it can be shownthat the following equation provides a reasonable approximation toequation 11: ##EQU4## where f is the focal length of the diffractivepower of the lens. As an alternative approximation the zone radii may becalculated by solving the following equation for r_(n) :

    r.sub.n.sup.2 =r.sub.0.sup.2 +2nλf/μ-k.sup.2 f.sup.3 (λν/μ).sup.2

where ##EQU5##

FIG. 7 is a cross-sectional view of a biconvex lens, designatedgenerally as 70 utilizing the invention. A lens of the form of lens 70could be used as an intraocular lens. Lens 70 has a first side 72 and asecond side 74. Diffractive zones, such as central zone 76 and annularzones 78 and 80 are provided on side 74. As in the lenses of FIGS. 1through 6 the radius of central zone 76 may be chosen arbitrarily inorder to provide the best functionality for a particular patient. Ifside 74 is the anterior side of the lens, equation (11) or equation (12)may be used directly to calculate zone radii with correction for theradius of curvature of the surface. If side 74 is the posterior side,those equations may be used by regarding the radius of curvature of thesurface as negative.

What is claimed is:
 1. A multifocal ophthalmic lens having opticalpower, at least a portion of said optical power being produced bydiffraction, said lens having a plurality of diffractive zones includinga central zone and a plurality of concentric annular zones, said centralzone having a radius r₀ and the innermost of said annular zones having aradius r₁ where r₀ ² is not equal to r₁ ² -r₀ ².
 2. The ophthalmic lensof claim 1 wherein said lens is an intraocular lens.
 3. The ophthalmiclens of claim 1 wherein said lens is a contact lens.
 4. The ophthalmiclens of claim 1 wherein said lens is an artificial cornea.
 5. Theophthalmic lens of claim 1 wherein said lens is an intralamellarimplant.
 6. The ophthalmic lens of claim 1 wherein r₀ ² is less than r₁² -r₀ ².
 7. The ophthalmic lens of claim 1 wherein r₀ ² is greater thanr₁ ² -r₀ ².
 8. The ophthalmic lens of claim 1 wherein said zones areseparated by optical steps having an optical height of one halfwavelength for light of a design wavelength.
 9. The ophthalmic lens ofclaim 7 wherein said design wavelength is in the spectral region of thegreatest photopic sensitivity of the human eye.
 10. The ophthalmic lensof claim 1 wherein said diffractive zones are provided on a curvedsurface.
 11. The ophthalmic lens of claim 10 wherein said zones haveradii that are corrected for the curvature of said curved surface. 12.The ophthalmic lens of claim 10 wherein said curved surface is concave.13. The ophthalmic lens of claim 12 wherein said zones have radii thatare corrected for the curvature of said curved surface.
 14. Theophthalmic lens of claim 13 wherein said zones are separated by stepshaving an optical height of one half wavelength for light of a designwavelength.
 15. The ophthalmic lens of claim 10 wherein said curvedsurface is convex.
 16. The ophthalmic lens of claim 15 wherein saidzones have radii that are corrected for the curvature of said curvedsurface.
 17. The ophthalmic lens of claim 16 wherein said zones areseparated by steps having an optical height of one half wavelength forlight of a design wavelength.